Question

Find the linear approximation of the function f(x) = √4-x at a = 0 and use it to approximate the numbers √3.9 and √3.99 ?

Answer 1

Answer:

1.9975

Step-by-step explanation:

The computation of the linear approximation of the given function is shown below:

L(x) = 2 - 1 ÷ 4(x)

As we are looking for √3.9

So here

x = 0.1

So

= 4 - 0.1

= 3.9

Now

L(0.1) = f(3.9) = 2 - (0.1 ÷ 4)

= 1.975

now

substitute the x = 0.01

Then

L(0.01) = f(3.99) = 2 - (0.01 ÷ 4)

= 1.9975

We simply applied the above equations